Achieving predictive light control over quantum materials requires detailed, real-time knowledge of their nonequilibrium states on ultrafast timescales. This capability is accessed through pump-probe techniques, where a high-intensity laser pulse disrupts the equilibrium state, and a weaker probe pulse tracks the evolving response. These spectroscopies uniquely provide insights into both time and energy aspects of the material’s behavior. However, nonequilibrium conditions introduce theoretical complexities beyond equilibrium models, requiring simultaneous consideration of intrinsic correlation functions and extrinsic probe wavefunctions to accurately interpret results.

Our group is dedicated to developing rigorous microscopic theories for a range of pump-probe spectroscopies, such as time-resolved resonant inelastic x-ray scattering (trRIXS), time-resolved x-ray absorption (trXAS), time-resolved Raman scattering, and time-resolved ARPES. A central area of interest is understanding nonlinear phenomena in pump-probe experiments, including finite-lifetime effects in trRIXS, high harmonic generation, and two-photon processes. To meet the demands of studying correlated materials, we also design wavefunction-based quantum many-body methods that numerically simulate these spectroscopies, enhancing our ability to interpret and anticipate experimental findings. These methods help bridge theoretical models with cutting-edge experimental techniques, advancing our understanding of nonequilibrium quantum materials.

A critical question in quantum technology is how to quantify, design, and control entanglement. In quantum optics, tools like interferometry allow for direct measurement of entanglement entropy, but quantum materials lack such characterization techniques. Measuring many-body wavefunctions precisely and exerting full control over degrees of freedom remain significant challenges in this domain.

To approach these challenges, we employ entanglement witness methods, leveraging observable spectral properties to provide a lower bound on multipartite entanglement for both equilibrium and transient states. Our group’s research, grounded in pump-probe theory, focuses on linking these ultrafast spectral observables to reconstruct specific entanglement witnesses, including quantum Fisher information and cumulative reduced density matrices. By developing these connections, we aim to identify systems and mechanisms for light-controlled entanglement, opening new avenues for dynamic control.

Beyond instantaneous characterization, we investigate how nonequilibrium dynamics can reveal entangled quantum states in materials. Certain entangled states, such as quantum spin liquids, often lack clear signatures in traditional spectroscopy due to their subtle, low-energy characteristics. By harnessing the additional time-domain data captured through nonequilibrium dynamics, we aim to uncover distinctive properties of these elusive states, ultimately enhancing our ability to characterize, detect, and control complex entangled states in quantum materials.

When a material is driven by a laser field, its electronic states become dressed with photons, creating a hybridized system of light and matter. Under a continuous monochromatic light field, many nonequilibrium dynamics are effectively described through Floquet theory, which simplifies complex time-dependent quantum behaviors into a superposition of steady states. In this framework, the quasi-energies of these states are offset by multiples of the photon energy, with each steady state comprising dressed electrons and photons. This laser-driven system enables precise control over single-particle dispersions and interactions.

Our group explores the mechanisms enabling light-controlled interactions in correlated materials, with a particular focus on Floquet engineering of many-body states. In such systems, light-induced interactions— including spin exchange, Coulomb interaction, electron-phonon coupling, and spin-orbit coupling —allow for dynamic control over intrinsic microscopic parameters that are otherwise rigid in equilibrium. Using unbiased, wavefunction-based simulations, we investigate optimal pump conditions and timescales for approximating and stabilizing these nonthermal states. Through pump-probe simulations, we seek to detect the distinctive spectral fingerprints that characterize these engineered states.

Superconductivity represents a critical quantum phase with transformative applications in energy-efficient transport, medical imaging, and quantum computing. Yet, achieving coherent Cooper pairing typically demands extreme conditions, such as ultra-low temperatures or high pressures, which limit practical implementations. Recent advances in ultrafast laser techniques offer promising avenues to transiently modify electronic structures and many-body interactions, raising the potential to induce superconducting states at temperatures and pressures beyond established critical thresholds.

Our group investigates nonequilibrium strategies to stabilize superconductivity as metastable excited states. We are interested in both conventional superconductivity, where electron-phonon coupling is the primary pairing mechanism, and unconventional superconductivity driven by strong electronic correlations. To enable these investigations, we develop numerical methods that capture dynamics involving both strong correlations and robust electron-phonon couplings, facilitating a detailed study of potentially light-induced superconducting phases.